I. Introduction


Table 1.Sample for 5 randomly chosen households of the data set used in this study
TotalCreditLimit After_tax_income RRIFs
41000 185925 0
5000 35450 0
47500 42500 0
32000 33450 0
22000 57800 65000

II. Exploratory data analysis


Table 2: Summary for the Total credit limit on all credit cards owned
n min median mean max sd
10996 125 16500 23667.51 340000 25638.52
Figure 2. Distribution for the Total credit limit on all credit cards owned by members the household

Figure 2. Distribution for the Total credit limit on all credit cards owned by members the household

Figure 3. Distribution for the after-tax income of the household

Figure 3. Distribution for the after-tax income of the household

Figure 4. Distribution for the Registered retirement income funds (RRIFs)

Figure 4. Distribution for the Registered retirement income funds (RRIFs)

Figure 5. Interactive Scatterplot for the Total credit limit on all credit cards owned against after-tax income. The red line is the best fit line. The blue curve is the Loess curve.

Figure 6. Interactive Scatterplot for the Total credit limit on all credit cards owned against Registered retirement income funds (RRIFs). The red line is the best fit line. The blue curve is the Loess curve.


III. Multiple linear regression

i. Methods

Figure 7. Distribution for the Total credit limit on all credit cards owned raised to 0.333.

Figure 7. Distribution for the Total credit limit on all credit cards owned raised to 0.333.

Using the following model:

## svyglm(formula = TotalCreditLimit_transf ~ RRIFs + After_tax_income, 
##     design = survey_design)
Figure 8. Normal Q-Qplot for the Total credit limit on all credit cards owned raised to 0.333

Figure 8. Normal Q-Qplot for the Total credit limit on all credit cards owned raised to 0.333

Figure 9. Residuals distribution for the statistical model

Figure 9. Residuals distribution for the statistical model

Figure 10. Residuals graph for the fitted values, with a Lowess curve in blue and a horizontal line at zero in red.

Figure 10. Residuals graph for the fitted values, with a Lowess curve in blue and a horizontal line at zero in red.

Figure 11. Residuals graph for After-tax income, with a Lowess curve in blue and a horizontal line at zero in red.

Figure 11. Residuals graph for After-tax income, with a Lowess curve in blue and a horizontal line at zero in red.

Figure 12. Residuals graph for the Registered retirement income funds (RRIFs), with a Lowess curve in blue and a horizontal line at zero in red.

Figure 12. Residuals graph for the Registered retirement income funds (RRIFs), with a Lowess curve in blue and a horizontal line at zero in red.

Table 3: VIF table
x
RRIFs 1.015446
After_tax_income 1.015446

ii. Model Results and Interpretation

Our model is the following:

\[ \begin{aligned}\widehat{Y}_{TCL}^{1/3} =& b_{0} + b_{RRIFs} \cdot (x_1) + b_{ATI} \cdot (x_2) \\ = & 20.77 + 0.000006 \cdot (x_1) + 0.00005 \cdot (x_2) \end{aligned} \]


Table 4: Summary Table:
Observations 10996
Dependent variable TotalCreditLimit_transf
Type Survey-weighted linear regression
0.166212
Adj. R² 0.166060
Est. S.E. t val. p
(Intercept) 20.771786 0.267456 77.664254 0.000000
RRIFs 0.000006 0.000001 7.464255 0.000000
After_tax_income 0.000050 0.000003 14.746694 0.000000
Standard errors: Robust

\[\begin{aligned} H_0:&\beta_{0} = 0 \\\ \mbox{vs }H_A:& \beta_{0} \neq 0 \end{aligned}\] \[\begin{aligned} H_0:&\beta_{RRIFs} = 0 \\\ \mbox{vs }H_A:& \beta_{RRIFs} \neq 0 \end{aligned}\] \[\begin{aligned} H_0:&\beta_{ATI} = 0 \\\ \mbox{vs }H_A:& \beta_{ATI} \neq 0 \end{aligned}\]

Table 6: 95% Confidence intervals for the model coefficients.

##                         2.5 %       97.5 %
## (Intercept)      2.024758e+01 2.129599e+01
## RRIFs            4.655997e-06 7.971805e-06
## After_tax_income 4.319980e-05 5.644323e-05

iii. Inference for multiple regression

Table 7. ANOVA Table

## Anova table:  (Rao-Scott LRT)
## svyglm(formula = TotalCreditLimit_transf ~ RRIFs, design = survey_design)
##                     stats      DEff        df   ddf         p    
## RRIFs              5033.9     66.45      1.00 10994 < 2.2e-16 ***
## After_tax_income 136804.6    629.09      1.00 10993 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Table 8. The 95% Prediction intervals for the Total credit limit on all credit cards owned, raised to 0.333, where RRIFs = 0, 10, 10000, 500000, 1000000, respectively, for After-income tax median = 68625.
RRIF Point estimate SE
0e+00 24.19079 0.1009230
1e+01 24.19085 0.1009211
1e+04 24.25393 0.0993586
5e+05 27.34774 0.4120943
1e+06 30.50469 0.8289865

IV. Discussion

i. Conclusions

ii. Limitations

iii. Further questions


V. Citations and References